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16 May, 21:58

Juan wants to change the shape of his vegetable garden from a square to a rectangle, but keep the same area so he can grow the same amount of vegetables. The rectangular garden will have a length that is 2 times the length of the square garden, and the width of the new garden will be 16 feet shorter than the old garden. The square garden is x feet by x feet. What is the quadratic equation that would model this scenario?

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  1. 17 May, 00:00
    0
    Here is the model, but the Areas are not the same.

    Old = X*X = X^2 Area

    New = 2X * (X-16) = 2X^2-32X

    If the Areas are the same,

    2X^2 - 32X = X^2

    X^2 - 32X = 0

    X (X-32) = 0

    X = 32

    Old Area = 32x32 = 1024 ft^2

    New Area = 2 (32x32) = 32x32 = 1024 ft^2
  2. 17 May, 00:22
    0
    For the square, the area will be 4x4, which will equal 16 sq ft. Since Juan is wanting to turn it to a rectangle, he will have to use the equation 8x2.
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